The most thought of Scripture referencing women working outside the home is Titus 2:3b-5:
Should a Christian woman work outside the home?
They [older women] are to teach what is good, and so train the young women to love their husbands and children, to be self-controlled, pure, working at home, kind, and submissive to their own husbands, that the word of God may not be reviled.
Paul echoed the guidance in 1 Timothy 5:14:
So I would have younger widows marry, bear children, manage their households, and give the adversary no occasion for slander.
In somewhat of a contrast is the woman of Proverbs 31 who buys and manages fields (vs. 16) and sells products (vs. 18, 24). Lydia (Acts 16:14) and Priscilla (Acts 18:2-3) were both businesswomen and given as godly examples of women in the church.
While the Bible gives no absolute restriction on where a woman may work, it does provide a sense of priority. First and foremost, women are to look after the home. This doesn't mean that a woman cannot work outside the home, just that her priority is to make sure the home is running well. This is to be in conjunction with the husband's role in the family. First Timothy 5:8 tells men, "if anyone does not provide for his relatives, and especially for members of his household, he has denied the faith and is worse than an unbeliever." So, the husband's priority is to make sure the family has the financial support it needs, while the wife's is to make sure the home is orderly.
In most cases, especially in families with small children, the most convenient way to do this is for the wife to stay at home and the husband to work. This division of labor is matched by the general situations of men and women—both characteristically, as women often have more of the patience and grace needed to care for young children, and culturally, as men usually find it easier to make more money.
That being said, every family situation is different. A disabled or underemployed husband may find that the best way to provide for his family is to let his wife be the primary wage-earner. In such a case, he is still responsible for making sure his family is cared for—he just happens to not be the one bringing home the check. Similarly, if the wife works outside the home, she still needs to make sure the house is running smoothly. She may delegate tasks to other family members according to schedule and inclination, but it is still her responsibility.
There are two heart issues that are usually at the core of the discussion of whether a Christian woman should work outside the home. The first is that of money. Specifically, where do the financial needs of the family meet the parental needs of the children? There is no blanket answer for this; sometimes husbands get sick, but sometimes couples value a wealthy lifestyle more than the needs of their children. At the core, parents need to realize that God calls their children a blessing, then be more committed to raising their children than being financially well off.
The other heart issue is that of a woman's worth and place in the world. Working a job gives the opportunity for satisfaction, praise, and community, and the qualitative joy of setting goals and reaching them. It takes a strong personality to find the same satisfaction in being a stay-at-home mom. It also takes a great deal of submission to deny one's education and workplace potential to care for those who do not have the capacity to appreciate the sacrifice.
Whether a Christian woman should work outside the home depends on the personalities involved, the ages of the children, the situation, and God's leading. Part of being a Christian is the freedom from worldly expectations—we should feel the freedom to live a modest lifestyle without two incomes, the freedom to accept God's validation over the world's, and the freedom to do what's best for our families despite the voices from either side.
What are to be our top priorities in our family life?
What does the Bible teach about marriage?
What does it mean for wives to submit to their husbands?
Is God/the Bible sexist?
What should a Christian mother be like according to the Bible?
Truth about Life Decisions